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Of course, White has somewhat more “aggressive” drawing lines with 3) Kf4 (Kf6, etc.), but at the end of the day, that Rook pawn will not Queen. Obviously, with White to move, it’s an easy win, but with Black to move, it’s a draw after the Kf7, which Alena found above.

Visually, with white having no pawn moves that wait, you can find Kf7 because takes what I like to think of as the combination of a long distance direct opposition combined with the diagonal opposition. Specifically, black places his king where he can come to e6 if white plays to e4 taking the direct opposition with 1 square between the kings, can come to f6 if the white king comes to d4 taking the diagonal opposition with one square between them, and can come to e7 if white plays to e3 taking the long distance opposition with 3 squares between the kings.

However, it is important to note that black cannot repeat this initial combo opposition by playing subsequently to g7 in response to Ke3:

1. ……………Kf7!
2. Ke3 Kg7??
3. Ke4

And now the diagonal opposition from g6 isn’t effective…..

3. ………….Kg6
4. Ke5

And the black king has no access to g5 because of the white pawn on h4- he is forced again to try the diagonal opposition, but we now know this is worthless because white has gotten to the 5th rank with the black pawn…

The key is BK should hold the opposition against the WK and it is a draw.
The moment WK gains the opposition he wins. Also, WK cannot be allowed to reach the fifth rank when even if BK holds the opposition, it is of no avail as the WK will capture the h5 pawn and white wins.
The King wanting to gain opposition has to maintain a distance of 3 ranks between him and the opposite King. In this way, if the opposing King advances one rank, he moves up one rank to oppose it. The opposition can be direct on same file or indirectly through a diagonal opposition. However the King should not be more than 2 files away.
So …1….Kg7 loses to 2. Ke4. Kg6 (if…Kf6. 3. Kf4 ) 3. Ke5 gaining the opposition.
Similarly 1…Kf8/h8/g7. loses to 2. Ke4.
The only move is 1….Kf7 keeping 3 ranks between the kings and not more than 2 files away.